Hi Jennie, I've never known where the rather unusual names came from, which is why I noticed your Angel. My great-aunt however died about 15 years ago, and her son two years ago.
The family line is traced back to Mark Rainsford, who in 1700-01 was Mayor of Dublin, and who founded the brewery which later became Guinness when Mark's grandson had to sell it to pay off debts. There is still a Rainsford St and a Rainsford Sq in Dublin called after him.
There was a family tradition for several generations of giving the first son his father's name as a second name, and so if Frederick was Richard's son he would be likely to have been Frederick Richard - Hume was Hume Frederick, and his son (my father) was Patrick Hume.
You might find more of interest (including a little corroboration of the above) by looking at the Rainsford genealogy page.